Geodesic
Computation of the longest segment of a~given direction in a~simplex
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 147-152

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Let $S$ be a nondegenerate simplex in $\mathbb R^n$ and let $v$ be a nonzero $n$-dimensional vector. We give the computational formulas for the length and endpoints of the longest segment in $S$ parallel to $v$. 
@article{FPM_2013_18_2_a10,
     author = {M. V. Nevskii},
     title = {Computation of the longest segment of a~given direction in a~simplex},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {147--152},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a10/}
}
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M. V. Nevskii. Computation of the longest segment of a~given direction in a~simplex. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 147-152. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a10/